Charitable giving rose 13 percent last year, says a new study scheduled to be released Tuesday by a philanthropy research group that is trying to deliver estimates of donations far earlier than “Giving USA,” which has for decades been the most-cited source of data on how much Americans donate.

But that figure stunned some charity experts, who say it seems higher than what anecdotal reports suggest. It also attracted a slam from the authors of “Giving USA,” who say the estimates are so inaccurate they will skew American’s understanding of the state of philanthropy.

While “Giving USA” has not yet calculated how much giving changed in 2013, the two organizations disagreed on the total donated in 2012—to the tune of $50-billion.

The reason for the dueling findings is that the two groups use different approaches to estimate how much Americans give.

“Giving USA,” produced by Indiana University Lilly Family School of Philanthropy, relies in part on Internal Revenue Service records from the 30 percent of taxpayers who itemize their deductions to calculate a national giving figure. [Editor's note: The previous sentence corrects an inaccuracy; Giving USA previously relied on surveys of nonprofits but does not now. ] Its 2013 report is planned for June, based on a preliminary look at tax returns, and its researchers plan to revise it at least two times as more tax information becomes available.

The Atlas of Giving, on the other hand, uses a set of 65 formulations of demographic, economic, and market data to come up with its estimates.

The company says on its website that it has “25 PhD-level mathematicians, analysts, and statisticians” who helped develop the method, but the organization doesn’t divulge anything else about its methodology.

Conflict Over Accuracy

The two leaders of the research projects were quick to criticize each other’s approach.

The Atlas of Giving estimate is “fallacious, simplistic, and wrong,” says Patrick Rooney, an associate dean at the Indiana University philanthropy school.

It’s the “Giving USA” survey that is lacking, according to Rob Mitchell, the chief executive officer of the Atlas of Giving.

The university report, he says, “does not give a snapshot that’s representative of the entire giving universe.”

Mr. Mitchell says his new report will show that giving increased to a record high of almost $417-billion.

Last year, when the Atlas estimated $365.3-billion in charitable gifts, “Giving USA” pegged the number at a more modest $316-billion.

Mr. Rooney says “Giving USA” is more accurate because it has been reviewed by hundreds of other academics and is vetted by a panel of nonprofit and statistics experts who give the school the “intellectual horsepower to validate and cross-validate” its findings.

It is impossible to validate the “Giving Atlas” methods, Mr. Rooney says, because the private company refuses to divulge the formulas it uses to divine an estimate.

“We’ve stuck to the scientific method,” he says. “Part of the scientific method is being transparent.”

That method also may take a bit more time to compile.

On the Atlas of Giving website, Mr. Mitchell criticizes “Giving USA’s” use of tax returns from previous years. Not only does such an approach fail to capture giving not included in IRS filings, but it is also out of date, he says: “It’s like getting excited about reading a newspaper today that specializes in reporting the news events of 18 months ago.”

The Atlas of Giving boasts that its 12-month forecast, which uses similar methods, is highly accurate. But it forecast 1.6-percent growth for 2013 early in the year and then ended the year with an estimate of 13 percent.

“No one was expecting the tremendous and continuing surge in the stock market,” Mr. Mitchell says. “That played a big factor” in the surprising results.

The wide disparity in the two groups’ estimates creates a sense of confusion among nonprofits, according to some charity experts.

“The onus is on Atlas of Giving to explain why they’re departing so much from the giving indicator of record,” says Robert Sharpe, a Memphis-based fund-raising consultant.

Nonprofit board members use the reports to see how they measure up with similar charities, to craft strategies, and to hire and fire people based on how well they perform compared with similar nonprofits, says Mr. Sharpe.

“This is not harmless,” he says of the wide gap between the two groups’ results. “People’s lives are affected.”

Though Mr. Sharpe and others are reluctant to trust the Atlas of Giving figures, others are giving the company a chance.

“Giving USA’s” reliance on tax returns from previous years risk making it a “technological dinosaur,” says Paul Schervish, director of Boston College’s Center on Wealth and Philanthropy.

Because the Atlas has not made its methods public, it is impossible to test the group’s results. But Mr. Schervish, a former member of “Giving USA’s” Advisory Council on Methodology, credits the Atlas with providing a “real time” look at charitable donations.

“The Atlas is the future,” he says. “Whether it is the present needs to be seen by examining its methodology.”